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/**
* This program is free software: you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3 of the
* License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see
* <http://www.gnu.org/licenses/>.
*
* (c) Vincenzo Nicosia 2009-2017 -- <v.nicosia@qmul.ac.uk>
*
* This file is part of NetBunch, a package for complex network
* analysis and modelling. For more information please visit:
*
* http://www.complex-networks.net/
*
* If you use this software, please add a reference to
*
* V. Latora, V. Nicosia, G. Russo
* "Complex Networks: Principles, Methods and Applications"
* Cambridge University Press (2017)
* ISBN: 9781107103184
*
***********************************************************************
*
* This program computes the betweenness dependency of all the nodes
* of a graph, using Brandes' algorithm, and counting all the
* shortest paths originating from a set of nodes (potentially the
* whole set of vertices).
*
* References:
* U. Brandes. "A Faster Algorithm for Betweenness
* Centrality". J. Math. Sociol. 25 (2001), 163-177.
*
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "utils.h"
void usage(char *argv[]){
printf("********************************************************************\n"
"** **\n"
"** -*- bet_dependency -*- **\n"
"** **\n"
"** Compute the betweenness dependency of all the nodes of a **\n"
"** network due to the shortest paths originating from a set **\n"
"** of initial nodes. If no start node is specified, compute **\n"
"** the dependency due to all the nodes of the graph. If no end **\n"
"** node is specified, compute the dependency due to the nodes **\n"
"** between node_start and the last node of the graph. **\n"
"** **\n"
"** The dependency of each node is printed on standard output. **\n"
"** **\n"
"** **\n"
"********************************************************************\n"
"\n\n"
" This is Free Software - You can use and distribute it under \n"
" the terms of the GNU General Public License, version 3 or later\n\n"
" (c) Vincenzo Nicosia 2009-2017 (katolaz@yahoo.it)\n\n");
printf("Usage: %s <graph_in> [<node_start> [<node_end>]]\n\n" , argv[0]);
}
void add_predecessor(unsigned int **pred, unsigned int k){
(*pred)[0] += 1;
*pred = realloc(*pred, ((*pred)[0] + 1) * sizeof(unsigned int));
(*pred)[ (*pred)[0] ] = k;
}
/*
* Returns a list of dependencies
*/
double* compute_bet_dependency(unsigned int N, unsigned int *J_slap, unsigned int *r_slap,
unsigned int n_start, unsigned int n_end){
int i, j, k, w, idx, cur_node;
unsigned int *marked, **preds, *dist, *nj;
double *delta, *cB;
unsigned int d;
unsigned int n, nd, ndp;
dist = malloc(N * sizeof(unsigned int));
marked = malloc(N * sizeof(unsigned int));
preds = malloc(N * sizeof(unsigned int *));
nj = malloc(N * sizeof(unsigned int));
delta = malloc(N * sizeof(double));
cB = malloc(N * sizeof(double));
for (i=0; i<N; i++){
cB[i] = 0;
preds[i] = NULL;
}
for (j=n_start; j<=n_end && j<N; j++){
for(i=0; i<N; i ++){
dist[i] = N;
if (! preds[i]){
preds[i] = malloc(sizeof(unsigned int));
}
preds[i][0] = 0; /* The list of predecessors is now empty! */
nj[i] = 0;
delta[i]= 0;
}
dist[j] = 0;
nj[j] = 1;
marked[0] = j;
d = 0;
n = 0;
nd = 1;
ndp = 0;
while (d<N && nd > 0){
for(i = n; i< n+nd; i ++){
cur_node = marked[i];
for (k=r_slap[cur_node]; k<r_slap[cur_node +1] ; k++){
w = J_slap[k];
if ( dist[w] == d+1){
add_predecessor((unsigned int **)(preds + w), cur_node);
nj[w] += nj[cur_node];
}
if ( dist[w] == N){
dist[w] = d+1;
marked[n + nd + ndp] = w;
add_predecessor(preds + w, cur_node);
ndp +=1;
nj[w] += nj[cur_node];
}
}
}
n = n + nd;
nd = ndp;
ndp = 0;
d += 1;
}
for (k= n-1; k>=1; k--){
w = marked[k];
for (idx=1; idx <= preds[w][0]; idx ++ ){
i = preds[w][idx];
delta[i] += 1.0 * nj[i] / nj[w] * (1 + delta[w]);
}
cB[w] += delta[w];
}
}
free(dist);
free(marked);
for (i=0; i<N; i++){
free(preds[i]);
}
free(preds);
free(nj);
free(delta);
return cB;
}
void dump_cB(double *cB, unsigned int N){
unsigned int i;
for (i=0; i<N; i++){
printf("%g\n", cB[i]);
}
}
int main(int argc, char *argv[]){
unsigned int *J_slap=NULL, *r_slap=NULL;
unsigned int K, N;
unsigned int n_start, n_end;
double *cB;
FILE *filein;
n_start = 0;
n_end = -1;
switch (argc){
case 4:
n_end = atoi(argv[3]);
case 3:
n_start = atoi(argv[2]);
case 2:
break;
default:
usage(argv);
exit(1);
break;
}
if (!strcmp(argv[1], "-")){
/* take the input from STDIN */
filein = stdin;
}
else {
filein = openfile_or_exit(argv[1], "r", 2);
}
read_slap(filein, &K, &N, &J_slap, &r_slap);
if (n_end == -1)
n_end = N-1;
cB = compute_bet_dependency(N, J_slap, r_slap, n_start, n_end);
dump_cB(cB, N);
free(cB);
free(J_slap);
free(r_slap);
}
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